Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#33791 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
574 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,21)(23,29)(24,33)(25,28)(27,40)(30,44)(32,49)(34,46)(35,52)(36,51)(38,39)(41,42)(43,48)(45,53)(47,50);(14,16,17,21)(15,18,19,20)(22,23)(24,34)(25,37)(26,29)(27,32)(28,31)(30,36)(33,44)(35,45)(38,49)(39,43)(40,48)(41,53)(42,47)(46,51)(50,52);(16,21)(18,20)(22,24)(23,30)(25,35)(26,36)(27,41)(28,42)(29,34)(31,45)(32,50)(33,40)(37,47)(38,51)(39,52)(43,53)(44,49)(46,48);(15,19)(18,20)(22,25,26,28)(23,31,29,37)(24,35,36,42)(27,38,39,40)(30,45,34,47)(32,48,43,49)(33,41,51,52)(44,50,46,53)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26779);